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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 87120bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.e3 | 87120bk1 | \([0, 0, 0, -2178, -35937]\) | \(55296/5\) | \(103317437520\) | \([2]\) | \(81920\) | \(0.85289\) | \(\Gamma_0(N)\)-optimal |
| 87120.e2 | 87120bk2 | \([0, 0, 0, -7623, 215622]\) | \(148176/25\) | \(8265395001600\) | \([2, 2]\) | \(163840\) | \(1.1995\) | |
| 87120.e4 | 87120bk3 | \([0, 0, 0, 14157, 1221858]\) | \(237276/625\) | \(-826539500160000\) | \([2]\) | \(327680\) | \(1.5460\) | |
| 87120.e1 | 87120bk4 | \([0, 0, 0, -116523, 15309162]\) | \(132304644/5\) | \(6612316001280\) | \([2]\) | \(327680\) | \(1.5460\) |
Rank
sage: E.rank()
The elliptic curves in class 87120bk have rank \(1\).
Complex multiplication
The elliptic curves in class 87120bk do not have complex multiplication.Modular form 87120.2.a.bk
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
